Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Thermal transport in the Falicov-Kimball model

James K. Freericks, V. Zlatić

Published Dec 10, 2001• 32 citations
Publisher

Abstract

We prove the Jonson-Mahan theorem for the thermopower of the Falicov-Kimball model by solving explicitly for correlation functions in the large dimensional limit. We prove a similar result for the thermal conductivity. We separate the results for thermal transport into the pieces of the heat current that arise from the kinetic energy and those that arise from the potential energy. Our method of proof is specific to the Falicov-Kimball model, but illustrates the near cancellations between the kinetic- and potential-energy pieces of the heat current implied by the Jonson-Mahan theorem.

DOI
10.1103/physrevb.64.245118

Related papers

Jonson-Mahan theorem

V. Zlatić, R. Monnier

This chapter proves the Jonson-Mahan theorem, which is a generalization of the result for noninteracting systems that all transport coefficients can be derived from integrals over frequency ω of a single transport function multiplied by different powers of ω. The Jonson-Mahan theorem extends this to many-body systems with a local (on-site) interaction, as contained, for example, in the Hubbard, Falicov-Kimball, and periodic Anderson models. This theorem is of great importance, because correlation functions involving the energy current density operator are extremely difficult to obtain by other means for interacting electrons. The proof starts from the observation that they are given by appropriate limits and derivatives of a time-ordered correlation function involving four variables, which are then calculated explicitly.

Oxford University Press eBooks•May 22, 2014•0 citations

Thermodynamics of the one-dimensional half-filled-band Falicov-Kimball model

Cláudio Andrade Macedo, L. G. Azevedo, André M. C. Souza

In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.

Physical review. B, Condensed matter•Oct 25, 2001•20 citations

Exact solution of the extended Falicov-Kimball model in the limit of zero conduction band width

Canio Noce, Alfonso Romano

A method for solving exactly the Falicov-Kimball model in the limit of vanishing conduction band is proposed. By means of the path integral formalism, a general procedure for the evaluation of the exact n-point Green functions at a finite temperature is developed. The results obtained here represent a starting point for a perturbation expansion in the conduction electron band width.

Journal of Physics Condensed Matter•Nov 6, 1989•8 citations

Thermodynamics of the two-dimensional Falicov-Kimball model: A classical Monte Carlo study

Maciej M. Maśka, Katarzyna Czajka

The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.

arXiv:cond-mat/0504533•Physical Review B•Jul 17, 2006•76 citations

Ground-State Energy and Low-Temperature Behavior of the One-Dimensional Falicov-Kimball Model

C. Gruber, Joel L. Lebowitz, Nicolas Macris

We consider the Falicov-Kimball model in the case of an equal number of classical "nuclei" and quantum "electrons" with Fermi statistics. In one dimension we find an exact formula for the leading behavior of the ground-state energy as a function of the attractive potential U between electrons and nuclei. For U > U c the system forms "atoms" which have an effective repulsion between them. Similar results hold for a continuum model provided there is a sufficiently large hard core between the nuclei. Some low-temperature properties are also discussed.

Europhysics Letters (EPL)•Feb 1, 1993•10 citations

Correlated hopping in the Falicov-Kimball model: A large-dimensions study

Avraham Schiller

The Falicov-Kimball model with a correlated-hopping interaction is solved using an extended dynamical mean-field theory that becomes exact in the limit of large dimensions. The effect of correlated hopping is to introduce nonlocal self-energy components that retain full dynamics as $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\infty},$ thus introducing an explicit k dependence to the single-particle self-energy. An explicit solution for the homogeneous phase at $D=2$ reveals significant nonlocal dynamical contributions in the physically relevant regime of a moderately large correlated-hopping amplitude, indicating that important nonlocal correlations are omitted in Hubbard-like models upon neglecting the correlated-hopping interaction.

arXiv:cond-mat/9911118•Physical review. B, Condensed matter•Dec 15, 1999•27 citations
We prove the Jonson-Mahan theorem for the thermopower of the Falicov-Kimball model by solving explicitly for correlation functions in the large dimensional limit. We prove a similar result for the thermal conductivity. We separate the results for thermal transport into the pieces of the heat current that arise from the kinetic energy and those that arise from the potential energy. Our method of proof is specific to the Falicov-Kimball model, but illustrates the near cancellations between the kinetic- and potential-energy pieces of the heat current implied by the Jonson-Mahan theorem.
This chapter proves the Jonson-Mahan theorem, which is a generalization of the result for noninteracting systems that all transport coefficients can be derived from integrals over frequency ω of a single transport function multiplied by different powers of ω. The Jonson-Mahan theorem extends this to many-body systems with a local (on-site) interaction, as contained, for example, in the Hubbard, Falicov-Kimball, and periodic Anderson models. This theorem is of great importance, because correlation functions involving the energy current density operator are extremely difficult to obtain by other means for interacting electrons. The proof starts from the observation that they are given by appropriate limits and derivatives of a time-ordered correlation function involving four variables, which are then calculated explicitly.
In order to contribute to understand well the finite-temperature properties of the Falicov-Kimball model, we study the temperature dependence of the specific heat, internal energy, entropy, and mean square fluctuation of the difference between the ion and electron numbers, and of the correlation functions of the one-dimensional half-filled-band Falicov-Kimball model. For this purpose we used the method of small-cluster exact-diagonalization calculations with the application of the grand canonical ensemble and of extrapolation techniques to the infinite chain. Our results show that the examined Falicov-Kimball model exhibits behavior of alternate electron-ion short-range ordering at low temperature, and gradual metal-insulator transition at high temperature, but, does not exhibit the crossing point of the specific heat curves, characteristic of the Hubbard model.
The two-dimensional Falicov-Kimball (FK) model is analyzed using the Monte Carlo method. In the case of concentrations of both itinerant and localized particles equal to 0.5 we determine temperature dependence of specific heat, charge density wave susceptibility, and density-density correlation function. In the weak interaction regime we find a first order transition to the ordered state and anomalous temperature dependence of the correlation function. We construct the phase diagram of half-filled FK model. Also, the role of next-nearest-neighbor hopping on the phase diagram is analyzed. Lastly, we discuss the density of states and the spectral functions for the mobile particles in weak and strong interaction regime.
We consider the Falicov-Kimball model in the case of an equal number of classical "nuclei" and quantum "electrons" with Fermi statistics. In one dimension we find an exact formula for the leading behavior of the ground-state energy as a function of the attractive potential U between electrons and nuclei. For U > U c the system forms "atoms" which have an effective repulsion between them. Similar results hold for a continuum model provided there is a sufficiently large hard core between the nuclei. Some low-temperature properties are also discussed.
The Falicov-Kimball model with a correlated-hopping interaction is solved using an extended dynamical mean-field theory that becomes exact in the limit of large dimensions. The effect of correlated hopping is to introduce nonlocal self-energy components that retain full dynamics as $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\infty},$ thus introducing an explicit k dependence to the single-particle self-energy. An explicit solution for the homogeneous phase at D=2D=2D=2 reveals significant nonlocal dynamical contributions in the physically relevant regime of a moderately large correlated-hopping amplitude, indicating that important nonlocal correlations are omitted in Hubbard-like models upon neglecting the correlated-hopping interaction.